The car-following behaviors of individual vehicles are defined by the Intelligent Driver Model (IDM) [1]}.
Through this model, the acceleration for a vehicle \(\alpha \)  is defined by its bumper-to-bumper headway \(h_\alpha \) , velocity \(v_\alpha \) , and relative velocity with the preceding vehicle \(\Delta v_\alpha \)  as:
\(\leavevmode \xbox {resizebox}{\XMLaddatt {width}{179.33922pt}f_\text{IDM} (h_\alpha , v_\alpha , \Delta v_\alpha ) = a \left[ 1 - \left( \frac{v_\alpha }{v_0} \right)^\delta - \left( \frac{s^*(v_\alpha , \Delta v_\alpha )}{h_\alpha } \right)^2 \right] + \epsilon }\) 
